What is ((x+2)^2}{25}+(\frac{(y+2))/9)^2=1 ?

The solution to ((x+2)^2}{25}+(\frac{(y+2))/9)^2=1 is Ellipse with (h,k)=(-2,-2),a=5,b=9

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((x+2)^2}{25}+(\frac{(y+2))/9)^2=1

\frac{( x + 2 ) ^{2}}{25} + (\frac{( y + 2 )}{9})^{2} = 1

(h, k) = (- 2, - 2), a = 5, b = 9

Solution steps

\frac{( x + 2 ) ^{2}}{25} + (\frac{y + 2}{9})^{2} = 1

Rewrite

\frac{( x + 2 ) ^{2}}{25} + (\frac{y + 2}{9})^{2} = 1

in the form of the standard ellipse equation

\frac{( x - ( - 2 ) ) ^{2}}{5 ^{2}} + \frac{( y - ( - 2 ) ) ^{2}}{9 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 2, - 2), a = 5, b = 9

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 2, - 2), b = 9, a = 5

\frac{( x - 3 ) ^{2}}{7} + \frac{y ^{2}}{15} = 1

x^{2} - 6 x + 4 y^{2} + 16 y + 21 = 0

\frac{( x + 3 ) ^{2}}{16} + \frac{( y - 1 ) ^{2}}{25} = 1

16 x^{2} + 36 y^{2} - 96 x + 36 y + 9 = 0

\frac{x ^{2}}{144} + \frac{y ^{2}}{16} = 1

What is ((x+2)^2}{25}+(\frac{(y+2))/9)^2=1 ?
The solution to ((x+2)^2}{25}+(\frac{(y+2))/9)^2=1 is Ellipse with (h,k)=(-2,-2),a=5,b=9